By Leondes, Cornelius T

ISBN-10: 0120127393

ISBN-13: 9780120127399

Meant for engineers, electric engineers and keep watch over engineers, this ebook presents assurance of the most recent advances in robot platforms, from the applying of neural networks to robotics

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**Additional info for Advances in robotic systems. Part 1 of 2**

**Example text**

Another difficulty which arises with specialized learning is that back- APPLICATIONS OF NEURAL NETWORK TO ROBOTICS 33 propagation cannot be used directly since the error arises at the output of the controlled system and not at the output of the neural network. It has been suggested that a solution to this problem is to have the errors propagate through the plant as if it were an additional layer with unmodifiable weights [33]. This leads back to the question of plant identification. A complete solution to the inverse dynamics problem has been presented by Kawato et al [17, 31].

Representation of A Collision-Free Path W e first introduce the via point representation of a path, where a r path is described b } a set of via points and is approximated by the line segments between the adjacent via points, as shown in Figure 22. This representation has two advantages: 1) we can achieve an arbitrary level of precision of a path by assigning a sufficient number of via points, 2) we can d e c o m p o s e the original problem into a set of uniform, small-sized tasks in which the relation between a point and obstacles is of a major concern, and 3) we can localize a path planning problem at individual via points, allowing massive parallel and distributed computing.

In the case where Τ is very small, the network acts like a switch: it produces " 1 " for a via point inside the obstacle, and " 0 " for a via point outside the obstacle. The shape of the surface of a collision penalty function becomes almost flat everywhere except near the obstacle boundary where a cliff appears. This makes via points hard to move along the surface. Using the re- lationship between the parameter Τ and the shape of the surface of a penalty function, we achieve the effect of simulated annealing b y slowly decreasing Τ from the sufficiently high temperature.

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